This article explores techniques for synthesizing resonant sounds using the principle of nonlinear distortion. These methods can be grouped under the heading of "subtractive synthesis without filters," the case for which has been made in the literature. Starting with a simple resonator model, this article looks at how the source-modifier arrangement can be reconstructed as a heterodyne structure made of a sinusoidal carrier and a complex modulator. From this, we examine how the modulator signal can be created with nonlinear distortion methods, looking at the classic case of phase-aligned formant synthesis and then our own modified frequency-modulation technique. The article concludes with some application examples of this sound-synthesis principle.